if rational no.s are closed under commutativity then -1/4 +5/4=1 and this is not a rational no.

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Solution

Commutative property for addition states that if a and b are two rational number then, a + b = b + a
-1/4 + 5/4 = 5/4 + -1/4
and 1 is also a rational number as it can be expressed as 1/1 in the form of p/q.

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Question 3
The numerical expression $\frac{3}{8} + \frac{(- 5)}{7} = \frac{- 19}{56}$ shows that:
(a) rational numbers are closed under addition.
(b) rational numbers are not closed under addition.
(c) rational numbers are closed under multiplication.
(d) addition of rational numbers is not commutative.

Question 4
Which of the following is not true?
(a) rational numbers are closed under addition.
(b) rational numbers are closed under subtraction.
(c) rational numbers are closed under multiplication.
(d) rational numbers are closed under division.

Q. (i) Are rational numbers always closed under division?
(ii) Are rational numbers always commutative under division?
(iii) Are rational numbers always associative under division?
(iv) Can we divide 1 by 0?

Q. Write 'T' for true and 'F' for false for each of the following:
(i) Rational numbers are always closed under subtraction.
(ii) Rational numbers are aways closed under division.
(iii) 1 ÷ 0 = 0.
(iv) Subtraction is commutative on rational numbers.
(v)

- (\frac{- 7}{8}) = \frac{7}{8} .

Question 5
$- \frac{3}{8} + \frac{1}{7} = \frac{1}{7} + (\frac{- 3}{8})$ is an example to show that
(a) addition of rational numbers is commutative.
(b) rational numbers are closed under addition.
(c) addition of rational number is associative.
(d) rational numbers are distributive under addition

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if rational no.s are closed under commutativity then -1/4 +5/4=1 and this is not a rational no.

Commutative property for addition states that if a and b are two rational number then, a + b = b + a -1/4 + 5/4 = 5/4 + -1/4 and 1 is also a rational number as it can be expressed as 1/1 in the form of p/q.

Commutative property for addition states that if a and b are two rational number then, a + b = b + a
-1/4 + 5/4 = 5/4 + -1/4
and 1 is also a rational number as it can be expressed as 1/1 in the form of p/q.